If it is a head wound, it is likely to bleed a lot. So it is often difficult to determine how serious the injury is. If the bleeding is easily controlled and the wound is small, it can most likely be treated with some topical antibiotic. If it is a larger cut or the bleeding cannot be controlled, it may require stitches and the dog should be taken immediately to a veterinarian.
Injuries to the body (e.g. throat, belly, legs) are often more serious and may indicate serious aggression. Unless the injury is very minor, the injured dog should go to a veterinarian and the dog that did the biting should be evaluated by a person who can make recommendations about handling or training the dog.